This topic has been covered to an extent on this page; however, it is such an interesting topic that it deserves attention here as well.
There are 4 aspects to dance helping you:
Dance is not the most strenuous of activities. However, it does demand complex movement and good posture. By simply working on moving well as you dance and maintaining good posture, you will increase your mobility and strength of the muscles you use to move. The end effect is a healthier body that moves with ease.
Dance is surprisingly good for your brain. When you dance you need to listen to the music, be aware of your partner, be aware of others on the floor and move your body. These actions all use different parts of your brain. Because these different parts are working in parallel, it is excellent brain exercise. This is why dance is so good at fighting dementia.
Many people make the comment that after a night of dancing they are alert, and need time to wind down before bed. Dance simply makes you feel good. The combination of physical and mental stimulation it offers leaves one feeling much better. Dance will make you a happier person.
We are talking about partner dance here. That means it is at least you and another person. Thus it is social from the get go. However, you often learn in groups, you will likely dance with a number of people in a night and you simply start talking with those around you. Dance will provide you with many social connections, and leave you a happier person for that reason.